Please answer the following questions:

Section 3 |Simple Harmonic Motion 25 Marks Q7. A homogeneous cylinder is connected to two identical springs as shown in the figure below: K K WWWWW m Figure 2 and it can rotate without sliding on a horizontal surface. The cylinder mass is m = 1 kg, the radius of the cylinder is r = 25 cm, the distance from the centre is a = 10 cm, and the spring constant is k = 10 N/m. The moment of inertia of the cylinder is I = = MR. Determine the period of the small oscillations. Hint: the cylinder rotates not around it's centre, but around the point of contact with the horizontal surface. That point should be the reference point. (Total 12 marks) Q8. A pendulum of length L and mass M is attached to a spring with spring constant k at a distance h below its point of suspension. Figure 3 k M Find the frequency of vibration (f = =) of the system for small angles 0. Assume the vertical suspension of length L is rigid but ignore its mass. The mass can be considered a particle, so I = ML2. (Total 13 marks)